Are vegetarians healthier people?

I've heard several people I've talked to recently state that vegetarians can't be all that healthy based on the lack of protein intake from a non-meat diet plus other factors. But, eating veggies for your entire diet is not inherently better than having some meat in your diet, right?

It all comes back to details. For example, there are a multitude of plant-based sources for protein -- it does not have to come from meat as some may think. Cutting out red meat (which is always a good idea) will reduce saturated fat and artery clogging, yes?

The only thing is that you can't replace meat in your diet -- if you decide to become a vegetarian -- with other foods that are bad for you.